The number of solutions of the equation $$\sin^{-1}\left[x^2 + \frac{1}{3}\right] + \cos^{-1}\left[x^2 - \frac{2}{3}\right] = x^2$$ for $$x \in [-1, 1]$$, and $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is:

A

2

B

0

C

4

D

Infinite